Carrier concentration optimization in semiconductor thermoelements

This paper considers the problem of carrier concentration optimization giving attention to the temperature dependence of the material parameters. The equations to be satisfied by the optimum constant and optimum variable carrier concentrations, in order to obtain maximum "average parameters" figure of merit are derived. The equations are obtained in general form so that they can be applied to any semiconductor model. In particular, the equations are solved for a nondegenerate extrinsic semiconductor. A comparison is made between the maximum "average parameters figures of merit" which can be obtained using optimum constant and optimum variable carrier concentrations, and the results interpreted in terms of available materials. A method is presented for the calculation of the optimum constant carrier concentration in a material when the thermoelectric parameters, as function of temperature, are known for a single sample with arbitrary constant carrier concentration. The results of the analysis are applied to the case of and type cast lead telluride. The optimum constant carrier concentration determined from the equations of the analysis and the one determined from the measurement of the materials parameters are compared in order to show the error to be expected by using the postulated model for the semiconductor material.